It would be interesting to have math historian compare this with other derivations of quadratic roots to assess its originality.
My favourite bit of knowledge about quadratic equations is that its roots can always be visualised as the intersection between a simple parabola (x^2) and a straight line (m*x + c).
In fact, the above is why imaginary numbers did not arise from needing to solve quadratic equations. Because in the case of complex roots, the line and the parabola simply do not interesect. So it was originally thought that there was no worthwhile solution anyway. The real 'need' for complex numbers arose from solving cubic equations. [1]
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It would be interesting to have math historian compare this with other derivations of quadratic roots to assess its originality.
My favourite bit of knowledge about quadratic equations is that its roots can always be visualised as the intersection between a simple parabola (x^2) and a straight line (m*x + c).
In fact, the above is why imaginary numbers did not arise from needing to solve quadratic equations. Because in the case of complex roots, the line and the parabola simply do not interesect. So it was originally thought that there was no worthwhile solution anyway. The real 'need' for complex numbers arose from solving cubic equations. [1]
[1] https://www.goodreads.com/book/show/19161684-a-friendly-appr...